Question about planet compression

[Peter1129]

So I recently found a statement about a character that could compress Earth to the size of a sugar cube due to the immense pressure within its body. So I was wondering can compression via gravity like in this blog be used for compression via pressure? Or is pressure and gravity different so there’s a different way to calculate planet compression via pressure?

And if compression via pressure is the same as compression via gravity than is this calc I made using the formula from that blog correct?

 

[Mr.Cutlery]

Bump because I'm also curious

 

[Peter1129]

Bump

 

[SheevShezarrine]

Bump

 

[DontTalkDT]

The answer is no, because that calc is completely wrong to begin with.
You notice that if you actually pay attention to the calc actually. The GBE of earth before compression is 2.24e32J and after compression is 2.24e33. So the change of GBE during compression is 2.24e32J - 2.24e33J = -2.016e33J.
The calc does it the wrong way, subtracting the GBE of earth from the GBE of the compressed earth.
The minus in the result is important because it means we actually don't consume energy, but that energy is released. At least, it's released if we only look at the GBE part of the process.
It makes sense, gravity pulls everything inwards. It tries to compress the earth, so it is actually helping us when we are compressing the planet. That is the result we get there: It tells us how much of the total work gravity would do for us in the compression process.

The reason we wouldn't actually gain energy from compression is of course because we have another force to work against that is much stronger than gravity. That force is the force between molecules that resists the matter that the earth is made of from being compressed. So we actually have to calculate how much work it is to compress the matter and then subtract the change in GBE.

Calculating the compression of matter is extremely difficult and since earth is an extremely complex object it is extra difficult.
The only maybe acceptable way to make a low-end estimate for it I can come up with is to approximate it via the compression of an ideal gas. (See this page and those linked within)
Edit: Then again, if you compress earth to sugar cube size I wonder if it would turn into a neutron star or something. No idea whether that would need special considerations.

 

[Peter1129]

Huh so that blog is wrong and unusable. Welp since I have no clue how to calc this stuff I guess I'll just have wait for somebody else on the calc request thread to calc it for me then.

Anyways thanks for the reply.

Edit: Wait so what tier would turning into a neturon star be? I assume it's either less than 4-B or only slightly above baseline right? Cause if that's the case then I guess I'll just remove the calc request on compression and just focus on its size.

Edit2: Found it. So it's just somewhat above baseline 4-B.

 

[Peter1129]

@DontTalkDT Anyways is there anybody you know that could calc this? Or should I just wait for somebody on the calc request thread to do it?

 

[DontTalkDT]

Edit: Wait so what tier would turning into a neturon star be? I assume it's either less than 4-B or only slightly above baseline right? Cause if that's the case then I guess I'll just remove the calc request on compression and just focus on its size.

Edit2: Found it. So it's just somewhat above baseline 4-B.

You can't really apply GBE of an average neutron star for this feat either. There is no real relation there.

@DontTalkDT Anyways is there anybody you know that could calc this? Or should I just wait for somebody on the calc request thread to do it?

I mean, I could. Not right now, since it's like 5am here, but maybe later. @Ugarik is the other person on the wiki from which I assume that they would have no problem doing the ideal gas version at least. Maybe he even has a better idea.

 

[Peter1129]

Ahh alright thanks. I guess I'll contact Ugarik since it seems like you don't have time.

 

[Ugarik]

First of all I want to say that I'm not 100% sure how to calculate it. But I do have an idea.

I don't know if solid matter and even be compressed it the first place. At least in that state. But compressing the substence will release a lot of heat which will eventually vaporize it, meaning the substence will turn into a gas state, which now can be compressed.

So my guess it that DT is actually more accurate than he thinks

 

[Ugarik]

@DontTalkDT
Aclually I noticed something important. It stated that it can compress the Earth to the size of a cusar cube. Can this be treated as blackhole creation since sugar cubes are smaller than Schwarzschild radius of Earth's mass?

 

[DontTalkDT]

@DontTalkDT
Aclually I noticed something important. It stated that it can compress the Earth to the size of a cusar cube. Can this be treated as blackhole creation since sugar cubes are smaller than Schwarzschild radius of Earth's mass?

Is the average sugar cube smaller? Schwarzschild radius of earth is 0.88cm... yeah, I guess it just barely is.

From the standpoint of physical concerns it could be treated as black hole creation I guess. Although, from a fictional standpoint I'm not sure whether we actually should take it as black hole creation as an ability if the says nothing of the sort.

 

[Peter1129]

I mean I couldn’t really find an average size for sugar cube when searching online. But from what most people told me it seems like the average length of a single sugar cube is just 1 cm so the radius would just be 0.5 cm. If anybody could find a better average size than I guess they could post it here.

 

[DontTalkDT]

Let me do the simple calc ignoring black hole creation business and go with ideal gas assumptions:

The initial volume is the volume of heart: Vi = 1.08321*10^21 m^3 (according to google)
The initial heat to use is more debatable. For the sake of a low end let's use average global surface temperature: T = 14°C = 287.15K
For the initial pressure let's use: Pi = 1 atm = 101325 Pa = 101.325 kPa
R = 8.31446261815324 J/(K * mol) be the ideal gas constant.
For the volume after compression, we assume: Vf = 1 cm^3 = 1e-6 m^3

Next, we have to decide on the formula. Realistically the result will be somewhere between isothermal and adiabatic compression. As we have no timeframe given, let's assume much of the heat can radiate away during the process and hence approximate with isothermal compression.
Hence the formula we wish to use is W = nRT*ln(Vf/Vi).
We know everything except n already.
The constant n can be calculate via the ideal gas law: PV = nRT, which one can rewrite to PV/(RT) = n. We want to use our initial constants to calculate, so we set P=Pi and V=Vi.
n = PiVi/(RT) = 101325 * 1.08321*10^21 /(8.31446261815324 *287.15) = 4.5971245199524130154748212636626018e22 mol

With that we can set into our work equation:
W = nRT*ln(Vf/Vi) = 4.5971245199524130154748212636626018e22 * 8.31446261815324 * 287.15 * ln(1e-6 / (1.08321*10^21) ) = -6.8322967317565033689058904003415604549381658604763144197894522284e27 J
The minus signifies that work is done on the object in this case (as the formula is for the work the gas does). So that would be our solution.

However, I see one immediate problem here. This is less than the work gravity would do for is (the change in GBE). That basically indicates that this approximation is too garbage to use. At least, unless I have made a mistake. Maybe some more high-end assumptions would be justified...

 

[Ugarik]

I'm not that knowledgeable in thermodynamics but what my intuition tells me is that the initial pressure and temperature are both wrong. I think you can compress a solid matter but you can't do it when it's in solid-state. You have to evaporate it first. And this pressure should cause enough heat to evaporate all the matter.

 

[DontTalkDT]

I'm not that knowledgeable in thermodynamics but what my intuition tells me is that the initial pressure and temperature are both wrong. I think you can compress a solid matter but you can't do it when it's in solid-state. You have to evaporate it first. And this pressure should cause enough heat to evaporate all the matter.

I think you can to an extent compress solids, but you are correct that they would soon vaporize.
That said, I don't think anything would prevent heat to dissipate while the matter is under pressure, so an isothermal compression should technically be possible.
I guess looking at adiabatic compression instead might still be a good idea.

If I use this calculator correctly and input the values I had already calculated for the prior calc I get -1.583832601893769*10^44 J
That does seem more plausible (about 1 Foe, which fits black hole creation cause supernova), I guess. We would still need to subtract the gravitational energy from that, but as usual that would probably not make much of a difference.

 

[Nerd1435]

I don't get why you thought of using ideal gas equation on a Solid object such as earth. (I mean it goes against every pre-requisite one could think of)
Unless you considered it is vaporized first before being compressed. Ideal gas equation on that still isn't a decent approximation but it's at least passable in that case.
But you also have to set the starting conditions accordingly instead of taking 1atm and avg. temperature of surface of earth.
And even after that it could be just some random polytropic process, information we have in hand is too less to estimate anything doing it this way.

 

[DontTalkDT]

I don't get why you thought of using ideal gas equation on a Solid object such as earth. (I mean it goes against every pre-requisite one could think of)
Unless you considered it is vaporized first before being compressed. Ideal gas equation on that still isn't a decent approximation but it's at least passable in that case.
But you also have to set the starting conditions accordingly instead of taking 1atm and avg. temperature of surface of earth.
And even after that it could be just some random polytropic process, information we have in hand is too less to estimate anything doing it this way.

The answer is because I'm doing low ends.
I take the assumptions the way I do because, while I don't know how to properly do it, these assumptions will almost definitely get a result lower than what the actual result would be. That means it is at least useable.

 

[Ugarik]

Well if the initial conditions are intentionaly wrong, the unreasonably low result shouldn't be a surprise

 

[DontTalkDT]

That's true. It really isn't.
I still like the approx. 1 FoE result for the case of it being done fast, though. It just fits my world view